4. A dry goods merchant failed, with liabilities amounting to $25000; his assets are: goods $9500, building and lot $5400, and bills collectible $2100; and the expense of settling will be 5% of the assets. How many cents on the dollar can he pay? 277. RULES.-1. To find what per cent. of his liabilities a bankrupt can pay, Divide the net proceeds of his assets by the amount of his liabilities, and the quotient expressed in hundredths will be the rate per cent. 2. To find the dividends of creditors in a case of bankruptcy, Multiply the several claims of creditors by the rate per cent. which the net proceeds of the assets will pay. NOTE. It is more common to find how many cents on the dollar the net proceeds will pay; the process is the same. INTEREST. PRELIMINARY DEFINITIONS. 278. Interest is the premium paid for the use of money. 279. The Principal is the sum of money for the use of which interest is paid. 280. The Amount is the sum of the principal and interest. 281. The Rate of Interest is the number of hundredths of the principal paid for its use one year. 282. The rate of interest fixed by law is called the legal rate; and any rate of interest higher than the legal rate is usury. The legal rate of interest in most of the states, and on debts due the United States, is 6%. In several states a rate higher than the legal rate is allowed, when so stipulated in the contract. (Art. 438.) 283. Simple Interest is interest on the principal only. Interest considers the element of time, in which respect it differs from the previous applications of percentage. For periods of time greater or less than one year, the interest is proportionally greater or less than the interest for one year. GENERAL METHOD OF COMPUTING INTEREST. MENTAL PROBLEMS. 1. When money is loaned at 6% a year, what part of the principal equals the interest for one year? Ans. Since 6 % .06, the interest for one year equals .06 of the principal. 2. What part of the principal equals the interest, when money is loaned at 5%? At 8%? At 10%? 3. What part of the principal equals the interest, when money is loaned at 4%? At 51 %? At 71% ? 4. What is the interest of $50 for one year at 6 %? SOLUTION.-Since the interest for one year, at 6 %, equals .06 of the principal, the interest of $50 for one year equals .06 of $50, which is $3. 5. What is the interest of $400 for one year at 7% ? At 8%? At 9%? At 10%? 6. What is the interest of $650 for one year, at 4%? At 6 %? At 8%? 7. What is the interest of $120 for one year, at 5%? At 5%? At 10%? 8. What is the interest of $250 for 3 years, at 6 %? SOLUTION.-The interest of $250 for year, at 6%, is $15, and since the interest for 1 year is $15, the interest for 3 years is 3 times $15, which is $45. 9. At 7%, what is the interest of $300 for 4 years? For 5 years? 10 years? 10. At 8%, what is the interest of $150 for 2 years? 4 years? 5 years? 8 years? 11. At 4%, what is the interest of $200 for 3 years? 4 years? 6 years? 12. At 10%, what is the interest of $25 for 6 years? 12 years? 8 years? 13. What is the interest of $70 for 2 years and 4 months, at 5% ? SUGGESTION.-4 months = of a year, and 2 yr. 4 mo. = 21 yrs. 14. At 4%, what is the interest of $15 for 3 years 3 months? For 5 years 6 months? 15. At 7%, what is the interest of $30 for 2 years 4 months? 3 years 2 months? 16. At 6%, what is the interest of $50 for 4 years 2 months? 6 years 10 months? 17. What is the interest of $10 for 4 years 6 months, at 4%? At 6%? At 9%? At 10%? 18. What is the interest of $500 for 3 years 2 months, at 5%? At 8%? At 12% ? WRITTEN PROBLEMS. 19. What is the interest of $145.60 for 5 years 10 months, at 5%? 20. What is the interest of $273.45 for 8 years 3 months, at 7%? At 10%? What is the interest of 21. $65.30 for 1 yr. 3 mo., at 6%? At 8%? 22. $640.58 for 4 yr. 11 mo., at 5%? At 10%? 23. $1000 for 1 yr. 1 mo., at 31%? 24. $85, at 7 %, for 3 yr. 7 mo.? At 7.3 % ? 25. $38.10, at 9%, for 6 yr. 5 mo. ? For 3 yr. 10 mo.? 26. $84.75 for 2 yr. 5 mo. 21 da., at 8% ? SUGGESTION.-Reduce the 5 mo. 21 da. to the decimal of a year. (Art. 171, N. 2.) 21 da. .7 mo., and 5.7 mo.= .475 yr. Hence, 2 yr. 5 mo. 21 da. =2.475 yr. 27. $208.44 for 7 yr. 8 mo. 15 da., at 5 %? 28. $356.75 for 5 yr. 10 mo. 24 da., at 61% ? 29. $184.80 for 1 yr. 1 mo. 10 da. (14 yr.), at 9% ? 30. $321.70 for 4 yr. 3mo. 27 da., at 121 %? What is the amount of 31. $60.85 for 10 yr. 10 mo. 10 da., at 10% ? 32. $740.10 for 1 yr. 1 mo. 18 da., at 8% ? 33. $1.40 for 7 yr. 11 mo. 21 da., at 71 % ? 34. $121.75 for 3 yr. 18 da., at 12 %? 35. $80.65 for 1 yr. 6 mo. 12 da., at 10% ? 36. What is the interest of $356.50 for 3 yr. 9 mo. 25 da., at 8%? PROCESS BY ALIQUOT PARTS FOR DAYS. 37. $84.66 for 5 yr. 7 mo. 20 da., at 5 %? 42. $2016.05 for 1 yr. 1 mo. 29 da., at 8 %? 43. What is the amount of $262.75 for 1 yr. 5 mo. 19 da., at 6 %? At 7%? At 9%? 44. What is the amount of $192.60 for 2 yr. 2 mo. 2 da., at 5%? At 10%? At 12% ? 45. A man borrowed $60 May 10, 1864, and paid it March 4, 1866, with interest at 6% what amount did hę pay? SUGGESTION.-Find the difference of time by compound subtrac tion. 46. What is the interest of $15.80, from Oct. 23, 1855, to Apr. 12, 1859, at 8 %? 47. A note of $565.80, dated June 3, 1864, was paid Nov. 28, 1869, with interest at 8% what was the amount paid? PRINCIPLE, FORMULA, AND RULE. 284. PRINCIPLE.-The principal multiplied by the rate per cent. equals the interest for one year. 285. FORMULA.-Interest-principal X rate % X time. 286. RULE. To find the interest of any sum of money for any time, at any rate per cent., 1. Multiply the principal by the rate per cent., expressed decimally, and multiply this product by the time in years and the fraction of a year. Or, 2. Multiply the interest for one year by the number of years, and of it by the number of months, and find the interest for days by aliquot parts. The sum of the several results will be the interest for the given time. NOTE. In solving the majority of problems in interest, the reduction of the months and days to the decimal of a year will be found as brief as the method by aliquot parts. Those who prefer to use aliquot parts, will find the method given above briefer than the one generally used. SIX PER CENT. METHOD. MENTAL PROBLEMS. 1. What is the interest of $1 for 2 years, at 6 %? SOLUTION.-The interest of $1 for 1 year at 6% is .06 of $1, which is 6 cents, and the interest for 2 years is 2 times 6 cents, which is 12 cents. |